Kenny joined the German outfit for the season and made 34 appearances - scoring two goals - as David Wagner led his side to a 12th place finish.
"Season finished for Schalke, it's been nothing but a pleasure to play for this club despite the ups and downs, I came here to play week in, week out and I want to say thanks for the manager for making that possible!" Kenny wrote on social media.
"Also to my team-mates who have been unbelievable with me helping to settle in as well as to play with such a good group of lads. Lastly I want to thank the fans for their unbelievable support home and away in every game, no matter how the game was going!
"It is something I definitely won't forget. Hopefully we'll see each other again!"